I'm trying to prove that (P → Q) ↔ (¬Q → ¬P) using Fitch.

I know I have to prove two subproofs.

1) P → Q 2)¬Q → ¬P

closed as off-topic by Joseph Weissman Jan 19 '16 at 0:17

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For the first part :

1) P → Q --- premise

2) ¬Q --- assumed [a]

3) P --- assumed [b]

4) Q --- from 1) and 3) by →-elimination

5) from 2) and 4)

6) ¬P --- from 3) and 5) by ¬-introduction, discharging [b]

7) ¬Q → ¬P --- from 2) and 6) by →-introduction, discharging [a].

The other part of the proof is similar.

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